In the past 15 years, topological phases of matters have become an active research topic in condensed
matter physics. Among these phases, there are gapped systems, such as topological insulators (TIs) and
topological superconductors (TSCs)[1]}, [2]}, [3]}, and gapless systems such as Weyl semimetals
(WSMs)[4]}, [5]} and various variants, e.g., anisotropic Weyl fermions[6]}, double
WSMs[7]}, [8]}, and tilted WSMs[9]}. For the TIs, the bulk topology are usually
indicated by some topological indices, and it is characterized by the monopole charges in the momentum
space for the WSMs. In these systems, the bulk topology is protected by some (global) symmetries[3]},
and thus are dubbed as the symmetry protected topological (SPT) phases. For these samples with boundaries,
there are gapless states localized at the edges, known as the bulk-boundary correspondence. These gapless
edge states is stable against symmetry-preserving perturbations.
